Completions index analysis

ABSTRACT

A method for determining a hydrocarbon-bearing reservoir quality prior to a hydraulic fracture treatment based on completions index is disclosed. The method comprises a step performing a test determining a hydraulic pressure at which a hydrocarbon-bearing reservoir will begin to fracture by pumping a fluid in a wellbore, wherein the wellbore extends from a surface to the reservoir and the wellbore has one or more perforations in communication with reservoir; a step generating a pressure transient in the wellbore, the pressure transient travels from the surface to the reservoir through the perforations and reflects back the surface after contacting the reservoir; a step measuring response of the pressure transient at sufficiently high sampling frequency; a step determining fracture hydraulic parameters of the perforations and the reservoir using the measured response; and optimizing a stimulation treatment to the reservoir based on the determined fracture hydraulic parameters.

FIELD OF THE INVENTION

The present invention relates to a method for determining ahydrocarbon-bearing reservoir quality, and in particular, to a methodfor determining a hydrocarbon-bearing reservoir quality prior to ahydraulic fracture treatment based on a completions index.

BACKGROUND OF THE INVENTION

Hydraulic fracturing is a technique of fracturing rock formations by apressurized fluid in order to extract oil and natural gas contained inthe formations. A fluid, which usually is water mixed with sand andchemicals, is injected into a wellbore under considerable pressure tocreate fractures in the formations. When the pressure is removed fromthe wellbore, the sand props the fractures open allowing the oil and gascontained in the formations to more readily flow into the well forextraction. This technique has revolutionized oil and gas development,especially is shale formations, because it permits extraction offormerly inaccessible hydrocarbons. As a result, it has helped push U.S.oil production to a new high and generate billions of revenues tomineral rights owners, oil companies, as well federal, state, and localgovernments.

Hydraulic fracturing, however, can be a very expensive process,especially if the quality of the formations is unknown. In ahorizontally drilled oil well, hydraulic fracturing generally isperformed in several stages along the horizontal portion of the well.Typically, the horizontal portion of the well is stimulated in stagesabout every 200 to 250 feet. Although the horizontal portion of the wellgenerally extends through a given hydrocarbon bearing formation, thelithology or rock quality may vary along the length of the wellbore.When oil companies conduct a frac treatment at a section of theformations that is sub-optimal, the stimulation may be ineffective orproduce marginal gains in productivity for that particular stage.Assuming that the average cost for each hydraulic fracture treatment isapproximately $100,000 and that some formations may have up to 80% ofits sections be sub-optimal, the cost and time spent in fracturingsub-optimal sections or in determining whether to move onto anothersection can be substantial. In one year, an energy consulting companyestimated that about $31 billion was spent in sub-optimal fracturingacross 26,100 U.S. oil wells.

Moreover, even if the oil drilling companies treat a section of theformation that happens to be optimal, the treatments may not have beenthe optimal size. In other words, the treatment may have been too smallgiven the favorable rock qualities that existed for that particularstage and that the well could have been even more productive and thereturn on the investment of the stimulation could have been even higherhad a larger stimulation been pumped, or had a different stimulationfluid or amount of proppant been pumped. As such, knowing the quality ofthe formations prior to a hydraulic fracture treatment is beneficial tostimulation treatments.

A method called Distributed Fiber Optic Sensing has been developed toprovide this information. This method is based on either temperature oracoustic sensing. In the method based on temperature sensing, a unitincluding a laser source and a photodetector is placed on the surfaceand a glass fiber is permanently installed in the well. The laser sourcesends laser pulses down the glass fiber and the temperature of theformations can affect the glass fiber and locally change thecharacteristics of light transmission in the glass fiber. Thephotodetector measures the laser light reflections from different spotsin the glass fiber due to the temperature and the spectrum of the laserlight reflections can used to determine the properties of theformations. The method based on acoustic sensing is similar to thetemperature sensing one except that this method employs a unit thatincludes an acoustic signal generator and an acoustic signal receiverand that this method measures the reflected acoustic signals based onthe strain or pressure of the formations exerted on and along variouspoints of the glass fiber. The measured acoustic signals may havevarious amplitude, frequency, and phase attributes that can also be usedto determine the properties of the formations.

The Distributed Fiber Optic Sensing method, however, has severaldrawbacks. First, this method requires running a glass fiber into thewell that complicates the installation process. Second, this methodusually costs around $600,000 to implement and the investment is onlyfor one single well and is permanent. Third, this method is noteconomically practical on smaller reservoir wells. Fourth, to protectthe fragile glass fiber, the glass fiber is typically placed within astainless steel sheath that can attenuate the temperature or strainresponse, reducing accuracy of the measurement.

Accordingly, there is a need for an improved method for determining thequality of the rock formations prior to a hydraulic fracture treatment.

SUMMARY OF THE INVENTION

In accordance with one embodiment of the present invention, a method fordetermining a hydrocarbon-bearing reservoir quality prior to a hydraulicfracture treatment based on a completions index is described.

The method comprises performing a test determining a hydraulic pressureat which a hydrocarbon-bearing reservoir will begin to fracture bypumping a fluid in a wellbore, wherein the wellbore extends from asurface to the reservoir and the wellbore has one or more perforationsin communication with the reservoir; generating a pressure transient inthe wellbore, the pressure transient traveling from the surface to thereservoir through the perforations and reflecting back the surface aftercontacting the reservoir; measuring the response of the pressuretransient at sufficiently high sampling frequency; determining thefracture hydraulic parameters of the perforations and the reservoirusing the measured response; and optimizing a stimulation treatment tothe reservoir based on the determined fracture hydraulic parameters.

In a preferred embodiment of the invention, the stimulation treatmentbeing optimized is a fracture treatment.

In one embodiment, the step of determining fracture hydraulic parametersof the perforations and the reservoir using the measured responsecomprises comparing the measured response to simulated responsesgenerated by an electrical model.

According to a preferred embodiment of the invention, the step ofdetermining the fracture hydraulic parameters of the perforations andthe reservoir comprising representing the fracture hydraulic parametersas a lumped impedance component containing a resistive element and acapacitive element.

According to another preferred embodiment of the invention, the step ofdetermining the fracture hydraulic parameter of the perforationscomprises determining a flow resistance of the perforations.

According to another preferred embodiment of the invention, the step ofdetermining the fracture hydraulic parameter of the reservoir comprisesdetermining a completions index of the reservoir.

In a preferred embodiment, the step of determining the fracturehydraulic parameter of the perforations is performed prior to the stepof determining the fracture hydraulic parameter of the reservoir.

In addition to the above steps, the method may further comprisegenerating additional pressure transients to determine closure offractures in the reservoir and reduction in completions index versustime.

In the step of determining fracture hydraulic parameters of theperforations and the reservoir using the measured response, the stepaccording to one embodiment may comprise numerically optimizing a neuralnetwork by extracting variables from the measured response as inputs.The variables are depth of the perforations for a given stage, rate ofdecay, slope ratio of the initial reflection to the incident reflection,and initial pressure drop in the test of determining a hydraulicpressure at which the reservoir will begin to fracture.

In the step of determining fracture parameters of the perforations andthe reservoir using the measured response, the step according to anotherembodiment may alternatively comprise numerically simulating a transientand using optimization methods through history matching to determinefracture hydraulic parameters.

In the step of generating a pressure transient, the step generates apressure transient by reducing or stopping the pump rate of pressurepumping equipment.

In the step of generating a pressure transient, the pressure transientmay be generated by stopping or reducing the pump rate of the surfacepressure pumping equipment, rapidly opening and closing a valve, oremploying a pressure oscillator or a mechanical shutter.

In the step of determining fracture hydraulic parameter of thereservoir, the determined fracture hydraulic parameter is related to asurface area inside the reservoir.

In addition to the above steps, the method may further comprisedetermining whether there is a hole in a casing of the wellbore.

According to a preferred embodiment, the pressure transient is generatedwithin the first 15 to 30 seconds of the test determining a hydraulicpressure at which a hydrocarbon-bearing reservoir will begin tofracture.

In the step of measuring response of the pressure transient atsufficiently high sampling frequency, the sufficiently high samplingfrequency is more than 2 Hz.

The step of optimizing a stimulation treatment to the reservoir based onthe determined fracture hydraulic parameters preferably comprisesadjusting the volume, properties or rate of the fracturing fluidrequired to fracture the reservoir, adjusting the volume or type of theproppant in the fracturing fluid, or omitting a particular stimulationtreatment.

In one embodiment of the invention, the performed test is a leakofftest.

In accordance with another embodiment of the present invention, a methodfor determining a hydrocarbon bearing reservoir quality is described.

The method comprises performing an initial leak-off test by pumping afluid in a wellbore using a pressure pumping equipment, wherein thewellbore extends from a surface to a hydrocarbon bearing reservoir andthe wellbore has one or more perforations in communication with thereservoir; creating a pressure transient in the wellbore, the pressuretransient travels from the surface to the reservoir through theperforations and reflects back the surface after contacting thereservoir, measuring a pressure-time plot at sufficiently high samplingfrequencies of the pressure transient traveling to the reservoir andreflecting back the surface; comparing the pressure-time plot toelectrical models representing different hydrocarbon bearing reservoirsand wellbores or numerically optimizing an electrical model to match thepressure-time plot; determining a flow resistance of the perforationsbetween the wellbore and the reservoir based on the comparison or thenumerical optimization; and determining a completions index of thereservoir based on the comparison or the numerical optimization.

In addition to the above steps, the method may further compriseoptimizing a stimulation treatment to the reservoir based on thedetermined flow resistance and completions index.

In a preferred embodiment of the invention, the stimulation treatmentbeing optimized is a fracture treatment.

In the step of determining the flow resistance based on the comparison,the flow resistance is determined by a rate of decay of thepressure-time plot.

In the step of determining the completions index based on thecomparison, the completions is determined by using shape of thepressure-time plot to solve a capacitance in the electrical models.

In the step of determining the completions index based on the numericaloptimization, the completions index is determined by a depth of theperforations for a given stage, the flow resistance, an initial pressuredrop in the leak-off test, and a slope ratio of a reflected rate ofchange to an initial rate of change.

In one embodiment of the invention, the flow resistance, the initialpressure drop, and the slope ratio are obtained from the pressure-timeplot.

In one embodiment of the invention, the flow resistance and the sloperatio are determined by finding values through numerical simulation tomatch the pressure-time plot. The slope ratio may be used to calculatethe completions index.

In one embodiment of the invention, the step of measuring apressure-time plot at sufficiently high sampling frequencies is measuredat frequencies higher than 2 Hz up to 500 Hz.

In the step of optimizing the stimulation treatment to the reservoir,the step comprises how much fluid and proppant are required to fracturethe reservoir.

In another embodiment of the invention, the method may further comprisegenerating multitude pressure transients during the course of a fracturetreatment to monitor or understand the effectiveness of the stimulationtreatment on the reservoir.

In the step of determining the completions index of the reservoir basedon numerical optimization, the step comprises interpolation by a neuralnetwork.

In another embodiment of the invention, the step of determining thecompletions index of the reservoir based on numerical optimizationcomprises optimizing a numerical model to match the measuredpressure-time plot.

In one embodiment of the invention, the step of determining the flowresistance based on numeral optimization and the step of determining thecompletions index of the reservoir based on numerical optimization occursimultaneously.

In addition to the above steps, the method may further comprisegenerating multitude pressure transients to compare most recentlydetermined flow resistance and completions index with prior determinedflow resistance and completions index.

In the step of determining the completions index, the step comprisescomparisons with previously obtained completions indices.

In one embodiment of the invention, the electrical model comprises anodal arrangement having impedance and resistive components representingan area of the reservoir, the wellbore, and the flow resistance.

In another embodiment of the invention, the method is performed after afracture treatment.

Since the present invention determines a hydrocarbon-bearing reservoirquality by analyzing a completions index, the present invention is alsoknown as Completions Index Analysis.

BRIEF DESCRIPTION OF THE DRAWINGS

For the purposes of illustrating the present invention, there is shownin the drawings a form which is presently preferred, it being understoodhowever, that the invention is not limited to the precise form shown bythe drawing in which:

FIG. 1 shows one embodiment of the method for determining ahydrocarbon-bearing reservoir quality.

FIGS. 2 and 3 show an example of a fracturing treatment having aleak-off test performed at the beginning of the fracturing treatment, aninitial water hammering effect of the leak-off test, and a final waterhammering effect after the fracturing treatment.

FIG. 4 is a closer or detailed view of the leak-off test shown in FIGS.2 and 3.

FIG. 5 shows an example of measured pressure transient response.

FIG. 6 shows an example of multiple pressure transients generated duringthe pressure decline of the leakoff test.

FIG. 7 shows that the measured pressure transient response can identifya hydrocarbon-bearing reservoir quality.

FIG. 8 shows that the measured pressure transient response can determineif there is a hole in the casing.

FIG. 9 shows a small section of an equivalent per unit length electricalmodel of a hydraulic wellbore/fracture system.

FIG. 10 shows matching between an electrical model response and anactual measured response for two different stages.

FIG. 11 shows the comparison of high Efficiency Coefficient and lowEfficiency Coefficient.

FIG. 12 shows the comparison of high completions index and lowcompletions index.

FIG. 13 shows the slope ratio variable for calculating the completionsindex and the correlation developed between slope ratios, initial slopeand stage depth.

FIG. 14 shows how the completions index changes throughout a fracturingtreatment.

FIG. 15 shows changes in Efficiency Coefficient and completions indexfrom initial water hammering to final water hammering.

DETAILED DESCRIPTION OF THE INVENTION

Referring to FIG. 1, one embodiment of the method for determining ahydrocarbon-bearing reservoir quality 100 is illustrated. The method 100comprises steps of performing a test determining a hydraulic pressure atwhich the reservoir will begin to fracture 110, generating a pressuretransient during the test 120, measuring response of the pressuretransient 130, determining fracture hydraulic parameters using themeasured response 140, and optimizing a stimulation treatment to thehydrocarbon-bearing reservoir based on the determined fracture hydraulicparameters 150.

The step of performing a test determining a hydraulic pressure at whichthe reservoir will begin to fracture, or a leak-off test, 110 involvespumping a fluid, for example a hydraulic fracturing fluid, into awellbore using a pressure pumping equipment. The wellbore extends from asurface to a reservoir and has one or more perforations extendingthrough the production casing in communication with the reservoir. Thepressure pumping equipment may be any equipment that is capable ofpumping the fracturing fluid at a pressure into the wellbore. Inaddition to determining the hydraulic pressure at which the reservoirwill begin to fracture, the leak-off test can also determine if theperforations are sufficiently open to establish communication with thereservoir. From the leak-off test, the ball seating pressure, thefracturing gradient (FG) of the formation, and the fracture closure timecan be determined. A leak-off test is illustrated in FIGS. 2 and 3.

FIGS. 2 and 3 show an example of a fracturing treatment having aleak-off test performed at the beginning of the fracturing treatment, aninitial water hammering effect of the leak-off test, and a final waterhammering effect after the fracturing treatment. Referring to FIG. 2,the fracturing treatment in which the leak-off test is performed has aduration of approximately three hours from start to finish. FIG. 3 is abreakdown of FIG. 2 that shows the treatment rate (the top graph), thetreatment pressure (the middle graph), and the proppant concentration(the bottom graph) of the fracturing treatment. The treatment rate inthis example is approximately 32 barrels per minute between about 0.45hour and 3.15 hour. The treating pressure is between 2,000 and 3,000 PSIfrom about 0.45 hour to 3.15 hour. The proppant concentration is between0.5 and 1 pound per gallon (PPA) from about 0.6 hour to 0.9 hour, andbetween 1.5 and 2 PPA from about 0.9 hour to 3 hour. The leak-off testis labeled as the “acid and leak-off test” in FIG. 2 or the graph priorto the “rise” or “step” at approximately 0.45 hour in the treatment rateand the treatment pressure graphs. The leak-off test is initiated andconcluded within approximately 30 minutes, or at about 0.5 hour, fromthe start of the fracturing treatment. After the leak-off test, and forthe remaining two and half hours, water with chemicals is pumping intothe wellbore and proppant is slowly added into the water to inject thestimulation fluid into the fractures in the reservoir.

Near the end of the leak-off test, a response or water hammering effectcan be measured by generating a pressure transient and monitoring howthe pressure transient declines with time. The very first 15 to 30seconds after generating the pressure transient shows a lot of noisewhen the pressure transient is measured under low sampling frequency,such as 1 Hz, and that is the water hammering effect of the pressuretransient. The pressure transient propagates to the perforations,reflects back to the surface, and travels in this manner back and forthuntil it attenuates completely. This response is shown as the initialwater hammering graph in FIGS. 2 and 3. The same response may also bemeasured at the end of the fracturing treatment and is shown as thefinal water hammering graph in the same figures. The final waterhammering graph shows more response or bounces because the fractures inthe reservoir have been opened.

FIG. 4 is a closer or detailed view of the leak-off test shown in FIGS.2 and 3. When the water hammering effect is measured at sufficientlyhigh sampling frequency, such as sampling frequencies higher than 2 Hzup to 500 Hz, more water hammering effect can be seen from themeasurement as shown in the plot labeled as “Water Hammering.” The shapeof the water hammering effect signal is directly depending upon the typeof rock in the reservoir in communication with the perforations and isan indication of the rock quality. Therefore, when the water hammeringeffect signal is showing a good shape, i.e., more fluctuations andslower attenuation, the oil company can pump in more stimulation fluidin that stage to extract more oil and gas. If the water hammering effectis showing a bad signal, i.e., less fluctuations and faster attenuation,the oil company can skip that stage or reduce the treatment size forthat stage saving thousands of dollars in fracturing treatment and moveonto the next stage. As such, the present invention provides real-timeknowledge about the rock quality that can vary in each stimulationtreatment stage of horizontal wellbores before the stimulation treatmentis performed. By understanding the water hammering effect signal in eachstage, oil companies can know when to pump more and when the pump lessof the stimulation treatment.

A leak off test, which is also known as mini-frac, is a pumping sequenceaimed to establish a hydraulic fracture, to understand, among otherthings, what is the pressure required to propagate a hydraulic fracture,and to estimate the minimum pressure at which the hydraulic fracturecloses. A critical component of the test is the pressure monitoringafter pumps as shut-down, which is commonly known as leakoff period orpressure fall off. During this period, fluid inside the open hydraulicfracture will leak off into the formation, continues until this processreaches a point that all fluid is leaked off and the hydraulic fracturecloses. Another component of the test is the “step rate test,” wherebythe rate of fluid is gradually increased at the beginning of the testuntil a fracture is established or reaches the fracturing extensionpressure and is reduced in a step down fashion at the end of the test.This test allows engineers to calculate the total pressure loss inbetween the rate steps so that the total number of perforationshydraulically connected to the fracture can be calculated. After thepumps are shut down, pressure is monitored for some time to determinefracture hydraulic parameters such as fracture closure pressure,presence of natural fractures, and leakoff coefficient for the fluid.Pressure may be monitored from several minutes to several hours and thefracture hydraulic parameters may be determined by using a “G” function.

Referring back to FIG. 1, the step of generating a pressure transient120, the pressure transient is preferably generated by stopping orsubstantially reducing the pump rate of the pressure pumping equipment.But optionally, the pressure transient can be introduced by othermethods that generate a pressure wave from the change of the inertia ofthe fluid, such as rapidly opening and closing a valve on the injectionwell head, or by other devices, such as a pressure oscillator or amechanical shutter. The pressure transient travels from the surface tothe reservoir through the perforations and reflects back to the surfaceafter contacting the reservoir at the speed of sound in the wellborefluid (normally water). Preferably, the pressure transient is generatedwithin the first 15 to 30 seconds of the test determining a hydraulicpressure at which the reservoir will begin to fracture. After thepressure transient attenuates, additional pressure transients can begenerated if desired (during the leak off test).

The response of the pressure transient, or the reflected pressuretransient, is measured at sufficiently high sampling frequency such asat least 5 Hz. Alternatively, sample frequencies higher than 2 Hz up to500 Hz may be used. The response is measured by a pressure transducer.An example of the measured response in high sampling frequency is shownin FIG. 5. The measured response is presented in a pressure-time plot.This measured response is also known as the water hammering effect. They-axis is the pressure in pounds per square inch (PSI) and the x-axis isthe time in minutes. The rounded dot represents the number of bouncesfrom the surface. “t” represents the travel time of the pressuretransient in sonic speed from the surface to the reservoir and then backto the surface through the wellbore fluid, which is the time between apeak and a trough on the plot. Such information can also be used todetermine the distance of the perforations from the surface since thetime between bounces is directly related to the distance to theperforations. A1 represents the initial decreasing amplitude of thewaveform and A2 represents the next decreasing amplitude. A1 generallyhas a larger amplitude than A2. Based on A1 and A2, the initial rate ofdecay, or Efficiency Coefficient (EC), can be calculated by thefollowing equation:

EC=√{square root over (A2/A1)}

Although FIG. 5 shows that A1 and A2 are the preferred amplitudes, anytwo successive decreasing amplitudes may also be used. With the measuredresponse in FIG. 5, fracture hydraulic parameters such as fractureclosure pressure, fracture closure time, presence of natural fractures,and resistance of the perforations can be determined. Additionally, theshape of the waveform, which is determined by the combination of t,amplitudes, slopes on the waveform from the ISP (Instantaneous Shut-inPressure) up to the A2 amplitude, can be used to calculate the fracturecapacitance of the reservoir. While FIG. 5 shows only one pressuretransient response, multiple pressure transients can be generated ineach stimulation stage to obtain multiple responses for determiningclosure of the fractures in the reservoir. This determination is basedon the comparison of the multiple responses with each other or thecomparison of the most recently obtained response (or the most recentlyobtained flow resistance and fracture capacitance, which are describedbelow) with a prior obtained response (or prior obtained flow resistanceand fracturing capacitance). FIG. 6 shows an example of thirteen (13)pressure transients generated during the pressure decline of the leakofftest. The closure of the fractures can be observed from the reduction ofthe Efficiency Coefficient of each pressure transient versus time (oruntil the Efficiency Coefficient and fracture capacitance of eachpressure transient no longer change with time). The figure showsresponses measured at 1 Hz and 250 Hz sampling frequencies. Responsesshowing inconspicuous fluctuations correspond to measurement at 1 Hzsampling frequency and responses showing pronounced fluctuationscorrespond to measurement at 250 Hz sampling frequency.

The measured response can identify reservoir quality. Measured responsesshow significant differences for different reservoirs or rocks havingsimilar wellbores (for example, multiple wells in a given field), as thepressure transient travels outside the wellbore through the perforationsof the wellbore and into the adjacent formation/rocks. If the transientpressure did not travel outside the wellbore, the expected responseswould be similar for comparable wellbores. This also proves that theperforations are open and in communication with the formation. Thisidentification ability is shown in FIG. 7. On the left of FIG. 7, asiliceous rich mud rock (shale), which has a lower Young's modulus and alower fracturing gradient, produces a lot of fluctuations or hammering(higher capacitance). On the right of FIG. 7, a carbonate rich mud rock(shale), which has a higher Young's modulus and a higher fracturinggradient, produces a lot less hammering (lower capacitance). Thus, basedthe amount of hammering, one can obtain an initial impression of whetherthe rocks are prone to simple or complex fracturing.

The measured response can also be used to determine if there is a holein the casing. Referring to FIG. 8, two wells A and B are plotted. WellA is represented by lighter-colored dots whereas Well B is representedby darker-colored dots. Well A has a casing without any holes and itsplot shows a pattern close to a linear line for the various stages wherepressure transients were measured. The slope m of the linear line may bedetermined by the following equation:

$m = \frac{\Delta \left( {{MD}\mspace{14mu} {Top}\mspace{14mu} {Perforation}} \right)}{\Delta \; t}$

MD top perforation is the measured depth to the top perforation. Theslope m is measuring the change in measured distance to the topperforation for successive stages in the well divided by the change intime. The slope m may also be determined by dividing the speed of soundC by 2.

Well B, on the other hand, has a casing with a hole and its dots spreadeverywhere on the chart without a general pattern. Based on the measuredresponse, it was confirmed by a downhole camera ran on this well that ahole was located in the casing at a measured depth of 6987 feet.

For every hydraulic wellbore/fracture model, there is an equivalentelectrical model. The wellbore or casing may be modeled as a lossytransmission line using resistors, capacitors, and inductors. The valuesof all these electrical components are known if one knows the depth ofthe well, the size of the casing, and the temperature and type of thefluid used in the well. Some or all of these values may be lumped intoan impedance representing the electrical property or mechanical propertyof the wellbore. The generated pressure transient inside the casing maybe modeled as an input voltage on the transmission line. Theperforations of the casing, which provide communication to thereservoir, may be modeled as a resistor. If the perforations are small,the resistance is high and vice versa. The reservoir itself or thequality of the reservoir may be modeled as a capacitor.

FIG. 9 represents a small section of an equivalent per unit lengthelectrical model. This small section of the electrical model correspondsto a small section of the horizontal portion of the wellbore. This smallsection of the electrical model is divided into three (3) nodes ((x−1),(x), and (x+1)) and each node is associated with a stub that is spacedalong the horizontal portion of the wellbore for example, every 30 feet.The stub associated with each node is used to represent an area of thereservoir and any changes in casing properties, otherwise the impedanceof the stub, Zs, is set sufficiently high such that no current flowsinto the stub. A simulated response similar to the actual measuredresponse can be obtained from each node by generating an input voltage,or simulated pressure transient, to the electrical model or circuit. Astub modeling a fracture, for instance, Zs(x+1) and Rs(x+1), representsfracture capacitance Zs(x+1) and flow resistance Rs(x+1). Eachimpedance, Zs(x−1), Zs(x), Zs(x+1), Z(x−1), Z(x), or Z(x+1), has aninductive component and a capacitive component and they are configuredto be the equivalent circuit of a transmission line (not shown). Whilefracture capacitance appears to be impedance, or Zs, in the figure, thevalue of the impedance is essentially capacitance. When the electricalmodel in FIG. 9 is simulated, the inductive component of Zs is treatedas if it has little to no inductance, and therefore, the impedancebecomes a capacitor representing an area of the reservoir or thefractures in that area of the reservoir. In other words, the electricalmodel by default presents or sees an area of the reservoir or thefractures in that area of the reservoir as impedance but the value ofthe impedance is simulated to be based on a capacitor. Although thisfigure shows only three nodes, there can be more nodes as this figurerepresents only a small section of the electrical model or thehorizontal portion of the wellbore. The distance between two adjacentnodes typically can range from 10 to 250 feet. Other ranges are alsopossible depending on the scale of the hydraulic wellbore system.

R(x−1), Z(x−1), and R(x) (and R(x), Z(x), and R(x+1), etc) are lumpedimpedance representative of a transmission line (Z(x−1)) and resistance(R(x−1) and R(x)) values and they represent a lateral portion of thecasing connecting adjacent nodes or adjacent areas of the reservoir. Allthese values are fixed and can be determined based on the depth of thewell, the size of the casing, and the fluid in the casing.

Therefore, by using an equivalent electrical model, one can obtain asimulated response similar to the actual measured response for eachstage of the horizontal portion of the wellbore. A simulated responsecan be created to match the actual measured response by adjusting theresistor in the stub and the capacitor of the impedance component in thestub or by solving their resistance and capacitance through numericaloptimization. Once the simulated response matches to the actual measuredresponse, the obtained resistance is known as the flow resistance andthe obtained capacitance is known as the fracture capacitance. FIG. 10shows such matching for two different stages. At stage X, the simulatedresponse (the top graph) matches to the actual measured response (thebottom graph) when the resistance is 33 ohm and the capacitance is 0.1farad. At stage Y, the simulated response matches to the actual measuredresponse when the resistance is 18 ohm and the capacitance is 1 farad.

Thus, by using an electrical model, simulated responses with theirassociated flow resistances and fracture capacitances can be obtainedfor previous actual fracture stimulation operations, future actualstimulation operations, and any other stimulation operations that onemay encounter since the information regarding the well, the casing, andthe fluid are already known, will be known, or can be predicted inadvance. All these simulated responses, flow resistances, and fracturecapacitances may be saved in a database or lookup table for comparisonwith future stimulation operations. In one embodiment, the comparisonmay be performed by adjusting the resistor in the electrical model firstto determine the flow resistance and then adjusting the capacitor todetermine the facture capacitance. Therefore, it is possible to modelevery expected response and different combination of depth, fractureflow resistance, fracture capacitance, and response at the surface interms of the pressure transient that is generated at the surface for agiven field. The benefit is that hydraulic properties of the fracturesystem of the reservoir can be inferred by just looking at the pressureresponses observed at the surface during the water hammering. The modelallows one to infer the flow resistance and the hydraulic capacitance ofthe fracture based on the pressure response measured at the surface. Inother words, if the comparison shows a match, the flow resistance andfracture capacitance of the actual fracture stimulation operation can beobtained from the flow resistance and fracture capacitance of thematched simulated response. With this lookup table, one does not need tomanually change the resistance and capacitance in the electrical modelfor matching its simulated response to every measured response. Thebenefit of having the lookup table or database allows an operator tocalculate these parameters very quickly. The operator can get thetransient response from the initial injection or leak off test beforethe primary stimulation of every stage in a horizontal wellbore, therebyproviding the operator valuable information needed on a near real timebasis to optimize each particular stage before pumping any proppant.

The flow resistance can also be approximated by the EfficiencyCoefficient. The Efficiency Coefficient is determined by how fast themeasured response decays (i.e., the initial rate of decay) and thenumber of bounces the measured response contains. These determiningfactors are directly related to the near wellbore flow resistance or theflow through the perforations. High Efficiency Coefficient means thatthe perforations are open and have less resistance, and low EfficiencyCoefficient means that the perforations are narrow and have moreresistance or that there is a tortuous path connecting the wellbore withthe hydraulic fracture. This is shown in FIG. 11.

The fracture capacitance is also known as the completions index. Thisvalue is directly related to the slope (darkened line) of the simulatedresponse as shown in FIG. 12, and it indicates whether the reservoir isa compliant or non-compliant system. Referring to FIG. 12, a positiveslope is considered as high index and it indicates that the reservoir isa compliant system. A negative slope is considered as low index and itindicates that the reservoir is a non-compliant system. A compliant ornon-compliant system provides information regarding how rigid thereservoir is. A compliant system means that the reservoir is less rigid(presence of natural fractures), the volume of a bounded fluid wouldexpand rapidly with increase in pressure and contact more surface areainside the reservoir. A non-compliant system means that the reservoir ismore rigid, the volume of a bounded fluid would remain relatively staticwith increase in pressure and contact less area inside the reservoir.Generally, a rock showing a compliant system is considered as good rockquality and is more ideal for a stimulation treatment. Conversely, arocking showing a non-compliant system is considered as lower rockquality and is less ideal for a stimulation treatment. As such, when oneobtains the completions index, or the value of the capacitance in thesimulated response, quality information of the reservoir is alsoobtained.

In addition to obtaining the fracture capacitance by comparing thesimulated responses to the measured response in the manner discussedabove, one can also obtain the fracture capacitance through numericaloptimization. One way of performing numerical optimization is via aneural network. In this invention, the neural network is a computationalmodel configured to receive four variables extracted from the measuredresponse, compares those variables to the same variables in thesimulated responses, and calculates the completions index if thecomparison matches. These four variables are the depth of thestimulation stage, the Efficiency Coefficient, the slope ratio, which ism1/m2 as shown in FIG. 13, and the initial pressure drop in the test ofdetermining a hydraulic pressure at which the reservoir will begin tofracture. FIG. 13 also shows the correlation developed between sloperatios, the initial slope, and the stage depth. The neural networkcompares the variables and calculates the completions index based ontraining weights obtained from simulations and previous measurements(optimizing a numerical model to match the measured response). Duringthis optimization, the Efficiency Coefficient and the completions indexare optimized together or simultaneously. The optimization of theEfficiency Coefficient simultaneously optimizes the completions indexand vice versa. The neural network may also be utilized to determine thefracture capacitance by interpolation. The employment of a neuralnetwork provides speedy comparison and calculation of the completionsindex.

Another way of performing numerical optimization to obtain the fracturecapacitance is via numerical simulation of the electrical model in FIG.9. One can use numerical optimization to match the electrical modeloutput to find a best fit to the measured field data. Using theequivalent per unit length electrical model shown in FIG. 9, one candetermine the correct flow resistance and completions index in order tomatch the observed field response. These values are found through aprocess of numerical optimization, wherein a numerical simulator solvesmany iterations of the electrical model output with varying flowresistance and completions index values. Each iteration is assigned afitness or a numerical value corresponding to the quality of the matchto the measured field response. The numerical simulator then outputs thevalues of the flow resistance and completion index with the best fitnessvalues. Like the numerical optimization based on a neural network, theflow resistance and fracture capacitance are also optimized together orsimultaneously. The optimization of the flow resistance simultaneouslyoptimizes the fracture capacitance and vice versa.

Therefore, referring to the step of determining fracture hydraulicparameters using the measured response 140 in FIG. 1, one can determineflow resistance and fracture capacitance by either comparing thesimulated response to the measured response with help from a lookuptable or employing numerical optimization. Based on the determined flowresistance and fracture capacitance, one can optimize a stimulationtreatment to the reservoir 150. The stimulation treatment may be ahydraulic fracturing treatment. The optimization of the stimulationtreatment may be adjusting the volume, properties or rate (i.e., numberof barrels per minute) of the fracturing fluid is required to fracturethe reservoir, adjusting the volume, size or type of proppant carried bythe fracturing fluid, or omitting a hydraulic fracturing treatmentaltogether for a given stage.

FIG. 14 shows how the completions index changes throughout a fracturingtreatment. In this example, the fracturing treatment is divided intothree phases instead of one single continuous fracturing treatment tobetter observe capacitance change and to adjust stimulation fluidaccordingly. Before any treatment is performed, the reservoir initiallyhas a completions index of 0.03. After the first phase of the fracturingtreatment is performed by pumping stimulation fluid with 92,000 lbs. ofsand and the pumping is shut down, which corresponds to the step of thepressure waveform to the left most of the plot, the completions index orcapacitance rises quickly to 0.087. This change in capacitance is anindication of the rock quality and can be used to optimize thefracturing treatment for a particular stage. The subsequent phases ofthe fracturing treatment show that increasing the amount of proppantyields minor increase in capacitance. As such, an operator knows howrigid the rock is and the optimal amount of proppant to fracture therock in this particular stage. Based on this figure, the operator maynot want to add any more proppant into the fluid after the second phaseor after the third phase since the completions index would not changemuch and the cost of fracturing treatment can be reduced. By analyzingthe completions index to determine reservoir quality, the method is alsoknown as Completions Index Analysis.

While FIG. 14 shows that the method of the present invention isconducted during a fracturing treatment, the method may also beperformed after the fracturing treatment to provide indications on thequality of the fracturing treatment just performed.

Based on the foregoing, using the measured responses from the waterhammering effect allows an operator to see the variations in the rockquality so one can recognize the good part of the lateral (i.e.,horizontal wellbore) and what is the poor part of the lateral. Knowingthis information, the operator can make near real time decisions tooptimize the stimulation treatments of the various stages of a wellbore.Thus, an operator can determine which sections of the wellbore mayjustify an even larger treatment than was originally planned and whichsections could be omitted, thereby reducing the overall cost of thetreatment and/or improving the effectiveness of the treatment.

FIG. 15 shows a comparison of the initial water hammering effect and thefinal water hammering effect for a stimulation stage based on theEfficiency Coefficient and the completions index. The initial waterhammering effect is the effect measured prior a fracture treatmentwhereas the final water hammering effect is the effect measured afterthe fracture treatment. Both have similar input slopes or utilizesimilar pressure transients. The final water hammering effect shows thatthe signal decays much slower after the fracture treatment, whichindicates that the fracturing fluid and the perforations have a betterconnection to the reservoir. The fracture treatment has eroded thetortuous path of the fractures and it becomes easier to establish acommunication from the wellbore to the reservoir. As such, both theEfficiency Coefficient and the completions index are higher after thefracture treatment. The Efficiency Coefficient before and after thefracture treatment are 0.814 and 0.897, respectively. The completionsindex before and after the fracture treatment are 0.235 and 0.820,respectively.

While the disclosure has been provided and illustrated in connectionwith a specific embodiment, many variations and modifications may bemade without departing from the spirit and scope of the invention(s)disclosed herein. The disclosure and invention(s) are therefore not tobe limited to the exact components or details of methodology orconstruction set forth above. Except to the extent necessary or inherentin the methods themselves, no particular order to steps or stages ofmethods described in this disclosure, including the Figures, is intendedor implied. In many cases the order of method steps may be variedwithout changing the purpose, effect, or import of the methodsdescribed. The scope of the claims is to be defined solely by theappended claims, giving due consideration to the doctrine of equivalentsand related doctrines.

What is claimed is:
 1. A method for determining a hydrocarbon-bearing reservoir quality comprising: performing a test determining a hydraulic pressure at which a hydrocarbon-bearing reservoir will begin to fracture by pumping a fluid in a wellbore, wherein the wellbore extends from a surface to the reservoir and the wellbore has one or more perforations in communication with the reservoir; generating a pressure transient in the wellbore, the pressure transient traveling from the surface to the reservoir through the perforations and reflecting back to the surface after contacting the reservoir; measuring the response of the pressure transient at a sufficiently high sampling frequency; determining fracture hydraulic parameters of the perforations and the reservoir using the measured response; and optimizing a stimulation treatment to the reservoir based on the determined fracture hydraulic parameters.
 2. The method according to claim 1, wherein the stimulation treatment is a fracture treatment.
 3. The method according to claim 1, wherein the step of determining fracture hydraulic parameters of the perforations and the reservoir using the measured response comprises comparing the measured response to simulated responses generated by an electrical model.
 4. The method according to claim 3, wherein the step of determining the fracture hydraulic parameters of the perforations and reservoir comprising representing the fracture hydraulic parameters as a lumped impedance component including a resistive element and a capacitive element.
 5. The method according to claim 1, wherein the step of determining the fracture hydraulic parameter of the perforations comprises determining a flow resistance of the perforations.
 6. The method according to claim 5, wherein the step of determining the fracture hydraulic parameter of the reservoir comprises determining a completions index of the reservoir.
 7. The method according to claim 6, wherein the step of determining the fracture hydraulic parameter of the perforations is performed prior to the step of determining the fracture hydraulic parameter of the reservoir.
 8. The method according to claim 6, further comprises generating additional pressure transients to determine closure of fractures in the reservoir and reduction in completions index versus time.
 9. The method according to claim 1, wherein the step of determining fracture hydraulic parameters of the perforations and the reservoir using the measured response comprises numerically optimizing a neural network by extracting variables from the measured response as inputs to the neural network.
 10. The method according to claim 9, wherein the variables are depth of a drilling stage, rate of decay, slope ratio of the initial reflection to the incident reflection, and initial pressure drop in the test of determining a hydraulic pressure at which the reservoir will begin to fracture.
 11. The method according to claim 1, wherein the step of generating a pressure transient generates a pressure transient by reducing or stopping the pump rate of a pressure pumping equipment.
 12. The method according to claim 1, wherein the step of generating a pressure transient generates a pressure transient by rapidly opening and closing a valve or by employing a pressure oscillator or a mechanical shutter.
 13. The method according to claim 1, wherein the determined fracture hydraulic parameter of the reservoir is related to a surface area inside the reservoir.
 14. The method according to claim 1, further comprising determining whether there is a hole in a casing of the wellbore.
 15. The method according to claim 1, wherein the step of generating a pressure transient occurs during the first 15 to 30 seconds of the test.
 16. The method according to claim 1, wherein the sufficiently high sampling frequency is more than 2 Hz.
 17. The method according to claim 1, wherein the step of optimizing a stimulation treatment to the reservoir based on the determined fracture hydraulic parameters comprises adjusting the volume, properties or rate of a fracturing fluid required to fracture the reservoir or the volume or type of proppant carried by the fracturing fluid, or omitting the stimulation treatment.
 18. The method according to claim 1, wherein the test is a leakoff test.
 19. A method for determining a hydrocarbon-bearing reservoir quality comprising: performing a leak-off test by pumping a fluid in a wellbore using a pressure pumping equipment, wherein the wellbore extends from a surface to a hydrocarbon bearing reservoir and the wellbore has one or more perforations in communication with the reservoir; creating a pressure transient in the wellbore, the pressure transient travels from the surface to the reservoir through the perforations and reflects back the surface after contacting the reservoir; measuring a pressure-time plot at sufficiently high sampling frequencies of the pressure transient traveling to the reservoir and reflecting back the surface; comparing the pressure-time plot to electrical models representing different hydrocarbon bearing reservoirs and wellbores or numerically optimizing an electrical model to match the pressure-time plot; determining a flow resistance of the perforations between the wellbore and the reservoir based on the comparison or the numerical optimization; and determining a completions index of the reservoir based on the comparison or the numerical optimization.
 20. The method according to claim 19, the method may further comprise optimizing a stimulation treatment to the reservoir based on the determined flow resistance and completions index.
 21. The method according to claim 20, wherein the stimulation treatment being optimized is a fracture treatment.
 22. The method according to claim 19, wherein the step of determining the flow resistance based on the comparison is determined by a rate of decay of the pressure-time plot.
 23. The method according to claim 19, wherein the step of determining the completions index based on the comparison is determined by using shape of the pressure-time plot to solve a capacitance in the electrical model.
 24. The method according to claim 19, wherein the step of determining the completions index based on the numerical optimization is determined by a depth of the perforations for a given stage, the flow resistance, an initial pressure drop in the leak-off test, and a slope ratio of a reflected rate of change to an initial rate of change.
 25. The method according to claim 24, the flow resistance, the initial pressure drop, and the slope ratio are obtained from the pressure-time plot.
 26. The method according to claim 19, the step of measuring a pressure-time plot at sufficiently high sampling frequencies is measured at frequencies higher than 2 hertz up to 500 Hz.
 27. The method according to claim 21, wherein the step of optimizing a stimulation treatment to the reservoir comprises how much fluid and proppant are required to fracture the reservoir.
 28. The method according to claim 21, further comprising generating multitude pressure transients during the course of the fracture treatment to monitor the stimulation treatment on the reservoir.
 29. The method according to claim 19, wherein the step of determining the completions index of the reservoir based on numerical optimization comprises interpolation by a neural network.
 30. The method according to claim 19, wherein the step of determining the completions index of the reservoir based on numerical optimization comprises optimizing a numerical model to match the measured pressure-time plot.
 31. The method according to claim 19, wherein the step of determining the flow resistance based on numeral optimization and the step of determining the completions index of the reservoir based on numerical optimization occur simultaneously.
 32. The method according to claim 19, further comprising generating multitude pressure transients to compare most recently determined flow resistance and completions index with prior determined flow resistance and completions index.
 33. The method according to claim 19, wherein the step of determining the completions index comprises comparisons with previously obtained completions indices.
 34. The method according to claim 19, wherein the electrical model comprises a nodal arrangement having impedance and resistive components representing an area of the reservoir, a lateral portion of the wellbore, and the flow resistance.
 35. The method according to claim 19, wherein the method is performed after a fracture treatment.
 36. The method according to claim 19, wherein the determined flow resistance and completions index are elements of a larger lumped electrical component. 